The University of Montana
Department of Mathematical Sciences

Technical report #5/2010

Regularization parameter selection for penalized-maximum likelihood methods in PET

J. M. Bardsley, Univ. of Montana
Marylesa Wilde, Univ. of Montana
Chris Gotschalk, U.C. Santa Barbara
M. S. Lorang, Univ. of Montana

Abstract

We present a software package for the supervised classification of images. By supervised, we mean that the user has in hand a representative subset of the pixels in the image of interest. A statistical model is then built from this subset to assign every pixel in the image to a best fit group based on reflectance or spectral similarity. In remote sensing, this approach is typical, and the subset of known pixels is called the ground-truth data.

Ideally, a classifier incorporates both spectral and spatial information. In our software, we implement quadratic discriminant analysis (QDA) for spectral classification and a choice of three spatial methods – mode filtering, probability label relaxation, and Markov random fields – for the incorporation of spatial context after the spectral classification has been computed. Each of these techniques is discussed with some detail in the text.

Finally, we introduce a graphical-user-interface (GUI) that facilitates the creation of ground-truth data subsets – based on individual pixels, lines of pixels, or polygons of pixels – that appear to the user to have spectral similarity. Once a ground-truth subset is created, histogram plots for each band are outputted in order to aid the user in determining whether to accept or reject it. Therefore the GUI makes the software quantitatively robust, broadly applicable and easily usable. We test our classification software on several examples.

Keywords: Markov random elds, probability label relaxation, quadratic discriminant analysis, remote sensing, supervised classi cation.

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